Spirographic Orbit of a Star in Extended Mass Distribution

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the orbit of a point mass through a Hernquist potential, which represents a star moving through a spherically symmetric extended mass distribution with a density profile of the form , where is the dimensionless radius and is the length scale of the potential. This type of mass density has been used to model physical systems such as dark matter halos, elliptical galaxies, and embedded young star clusters.

Contributed by: Ted Landis, Jeremy Spitzig, and Lisa Holden (March 2011)
Open content licensed under CC BY-NC-SA



is the dimensionless energy parameter.

is the dimensionless angular momentum parameter.

represents dimensionless time.


L. Hernquist, "An Analytical Model for Spherical Galaxies and Bulges," The Astrophysical Journal, 365, 1990 pp. 359–364.

F. C. Adams and A. M. Bloch, "Orbits in Extended Mass Distributions: General Results and the Spirographic Approximation," The Astrophysical Journal, 629, 2005 pp. 204–218.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.